The proposed work focuses on tqo areas of biostatistical methodology which have important application to cancer research. The first area deals with robustification of the Cox regression model. For the analysis of remission duration and survival data, the most widely used regression procedure is the Cox proportional hazards regression. Unfortunately, its estimation and testing procedures are very sensitive to outliers among the covariates. The goal of the proposed work is to develop a robust version of Cox regression in which the covariate values have bounded influence on both estimation and testing. The asymptotic distribution theory will be derived for the robust estimator, and the small and moderate sample size properties of the robust procedure will be compared with Cox's original regression by Monte Carlo methods. This same robustification procedure should extend to conditional logistic regression for the analysis of matched case-control studies. The second area deals with regression methods for matched-pair survival analysis. Such analyses are appropriate in clinical studies in which the tumor-free survival of differently treated paired organs, e.g. breasts, kidneys, and patches of skin, are to be compared. The proposed research focuses on the nonparametric (linear rank) approach to marginal models for matched data. So far these methods have been developed for the two-sample testing problem. The goal here is to extend these methods for estimation and hypothesis testing in the general regression problem. The asymptotic distribution theory will be derived. A study of the asymptotic relative efficiency of the proposed tests to each other and to parametric tests is planned, as is a Monte Carlo investigation of the small and moderate sample size properties of the estimators and test statistics.